Acoustics: an introduction to its physical principles and applications

Foreword......Page 8
Preface to the First and Second Editions......Page 11
Preface to the Third Edition......Page 15
Contents......Page 17
About the Author......Page 28
List of Symbols......Page 29
 Greek......Page 34
 Subscripts......Page 37
1 The Wave Theory of Sound......Page 38
 1.1 A Little History......Page 40
 1.2 The Conservation of Mass......Page 43
 1.3 Euler's Equation for a Fluid......Page 45
 1.4 Pressure–Density Relations......Page 48
  1.4.1 Laplace's Hypothesis......Page 49
  1.4.2 Interpretation in Terms of Entropy......Page 50
  1.4.3 Incorporation of Heat Conduction into FluidDynamics......Page 51
 1.5 Equations of Linear Acoustics......Page 52
 1.6 The Wave Equation......Page 55
  1.6.1 The Velocity Potential......Page 57
 1.7 Plane Traveling Waves......Page 58
  1.7.1 Processes Occurring During Passage of a SoundWave......Page 61
 1.8 Waves of Constant Frequency......Page 62
  1.8.1 Time Average of a Product......Page 64
  1.8.2 Spatially Dependent Complex Amplitudes......Page 65
  1.8.3 Plane Waves of Constant Frequency......Page 66
  1.9.1 Speed of Sound in Gases......Page 67
  1.9.2 Acoustic Properties of Liquids......Page 69
 1.10 Adiabatic Versus Isothermal Speeds......Page 74
  1.11.1 Acoustic-Energy Corollary......Page 76
  1.11.2 Energy Conservation in Fluids......Page 77
  1.11.3 Acoustic Power of Sources......Page 79
  1.12.1 Spherical Spreading of Acoustic Energy......Page 81
  1.12.2 Spherically Symmetric Solution of the WaveEquation......Page 83
  1.12.3 Fluid Velocity in a Spherically Symmetric Wave......Page 84
  1.12.4 Intensity and Energy Density......Page 85
  1.12.5 Field at Large Distances from Source of FiniteExtent......Page 86
 1.13 Problems......Page 88
  2.1.1 Frequency Bands......Page 98
  2.1.2 Frequency Partitioning of Mean Squared Pressure......Page 99
  2.1.3 Frequency Partitioning of Intensity, Acoustic Power, and Energy Density......Page 100
 2.2 Proportional Frequency Bands......Page 101
  2.2.2 Equally Tempered Musical Scales......Page 102
  2.3.1 Sound-Pressure Levels......Page 105
  2.3.3 Logarithms and Antilogarithms......Page 106
  2.3.4 History of the Decibel......Page 108
  2.3.5 Intensity and Power Levels......Page 110
  2.4.1 Frequency Weighting Functions......Page 111
  2.4.2 Linear Filters......Page 112
 2.5 Combining of Levels......Page 114
 2.6 Mutually Incoherent Sound Sources......Page 117
 2.7 Fourier Series and Long-Duration Sounds......Page 120
  2.7.2 Levels and Spectral Density......Page 122
 2.8 Transient Waveforms......Page 124
  2.8.1 Dirac Delta Function......Page 126
  2.8.2 Sound-Exposure Spectral Density......Page 128
 2.9 Transfer Functions......Page 129
 2.10 Stationary Ergodic Processes......Page 132
  2.10.1 Wiener–Khintchine Theorem......Page 134
 2.11 Bias and Variance......Page 137
 2.12 Problems......Page 143
 3.1 Boundary Conditions at Impenetrable Surfaces......Page 151
  3.1.2 Vibrating Surfaces......Page 153
  3.1.3 Continuity of Normal Component of Displacement......Page 155
 3.2 Plane-Wave Reflection at a Flat Rigid Surface......Page 156
 3.3 Specific Acoustic Impedance......Page 158
  3.3.2 Plane-Wave Reflection at a Surface with Finite Specific Impedance......Page 160
  3.3.3 Locally Reacting Surfaces......Page 162
  3.3.4 Theory of the Impedance Tube......Page 163
 3.4 Radiation of Sound by a Vibrating Piston Within a Tube......Page 166
  3.4.1 Causality......Page 167
  3.4.2 Tube with Rigid End: Resonance......Page 168
  3.4.3 Constant-Frequency Oscillations......Page 171
  3.4.4 Tube with Impedance Boundary Condition at End......Page 173
  3.4.5 The Q of a Resonance......Page 174
 3.5 Sound Radiation by Traveling Flexural Waves......Page 176
  3.5.2 Trace-Velocity Matching Principle......Page 177
  3.5.3 Outgoing Versus Incoming Waves......Page 179
  3.5.4 Acoustic Disturbances Created by Subsonic Flexural Waves......Page 180
  3.5.5 The Coincidence Frequency......Page 181
  3.5.6 Specific Radiation Impedance......Page 183
 3.6 Reflection and Transmission at an Interface Between Two Fluids......Page 184
  3.6.1 Water–Air Interfaces......Page 189
  3.6.2 Transient Reflection......Page 190
 3.7 Multilayer Transmission and Reflection......Page 192
  3.8.2 Slab Specific Impedance......Page 196
  3.8.3 Oblique-Incidence Mass Law......Page 199
  3.8.4 Transmission Through Euler–Bernoulli Plates......Page 200
  3.8.5 Transmission Through Porous Blankets......Page 203
 3.9 Problems......Page 204
 4.1 Radially Oscillating Sphere......Page 212
  4.1.1 Low-Frequency Approximation......Page 214
 4.2 Transversely Oscillating Rigid Sphere......Page 215
  4.2.2 Small-ka Approximation......Page 218
  4.3.1 Concept of a Point Source......Page 219
  4.3.2 Point Mass Source......Page 222
  4.3.3 Green's Functions......Page 223
  4.4.1 Dipoles......Page 226
  4.4.2 Point Force in a Fluid......Page 227
  4.4.3 Quadrupoles......Page 228
  4.4.4 Multipole Expansions......Page 231
  4.5.1 Poisson's Theorem and Its Implications......Page 233
  4.5.2 Closed Regions......Page 236
  4.5.4 Sommerfeld Radiation Condition......Page 239
  4.5.5 Uniqueness of Constant-Frequency Fields......Page 241
 4.6 The Kirchhoff–Helmholtz Integral Theorem......Page 243
  4.6.1 Multipole Expansions of the Kirchhoff–Helmholtz Integral......Page 245
 4.7 Sound Radiation from Small Vibrating Bodies......Page 246
 4.8 Radiation from a Circular Disk......Page 254
  4.8.1 Oblate-Spheroidal Coordinates......Page 255
  4.8.2 Solutions of Laplace's Equation......Page 256
  4.8.3 Determination of the Outer Solution......Page 258
  4.9.1 Reciprocity in Vibrating Systems......Page 259
  4.9.2 Reciprocity and the Linear Acoustic Equations......Page 261
  4.9.3 Interchange of Source and Listener......Page 262
  4.9.4 Reciprocity and Green's Functions......Page 263
 4.10 Transducers and Reciprocity......Page 264
 4.11 Problems......Page 268
  5.1.1 Image Sources......Page 275
  5.1.2 Remarks Concerning Acoustic Power and Spherical Spreading......Page 276
  5.1.3 Cases When More Than One Wall Is Present......Page 277
  5.1.4 Dependence of Acoustic Far Field and Net Acoustic Power Output on Distance from a Wall......Page 278
 5.2 Sources Mounted on Walls: The Rayleigh Integral; Fresnel–Kirchhoff Theory of Diffraction by an Aperture......Page 280
  5.2.1 Green's-Function Derivation of Rayleigh Integral......Page 282
  5.2.2 Fresnel–Kirchhoff Theory of Diffraction......Page 283
 5.3 Low-Frequency Radiation from Sources Mounted on Walls......Page 285
  5.3.1 Pressure on Vibrating Circular Piston at Low Frequencies......Page 286
  5.3.2 Force Exerted by the Slowly Oscillating BaffledPiston......Page 288
  5.4.1 Electroacoustic Significance of RadiationImpedance......Page 289
  5.4.2 Evaluation of Radiation Impedance for a Baffled Circular Piston......Page 290
 5.5 Far-Field Radiation from Localized Wall Vibrations......Page 295
 5.6 Transient Solution for Baffled Circular Piston......Page 298
  5.7.1 Field on Symmetry Axis......Page 302
  5.7.2 Field Near Symmetry Axis......Page 304
 5.8 Transition to the Far Field......Page 305
  5.8.1 Properties of the Diffraction Integral......Page 309
  5.8.2 Field Near Edge of Main Beam......Page 310
  5.8.3 Characteristic Single-Edge Diffraction Pattern......Page 312
  5.8.4 Field Far Outside the Central Beam......Page 316
 5.9 Problems......Page 317
6 Room Acoustics......Page 324
 6.1 The Sabine–Franklin–Jaeger Theory of Reverberant Rooms......Page 325
  6.1.2 Spatial Uniformity......Page 326
  6.1.3 Reverberation Time......Page 328
  6.1.4 Sabine's Equation......Page 329
  6.1.5 Diffuse Sound Fields......Page 331
  6.1.7 Absorbing Power of Objects and Persons......Page 334
  6.2.1 Mean Free Path......Page 336
  6.2.2 Limitations of Sabine's Equation......Page 338
  6.2.3 Norris–Eyring Reverberation Time......Page 339
  6.2.4 Rooms with Asymmetric Absorption......Page 341
  6.2.5 The Room Constant......Page 343
  6.3.1 Design and Correction of Rooms......Page 346
  6.3.2 Measurement of Absorption Coefficients and Reverberation Times......Page 349
  6.3.3 Measurement of Source Power......Page 351
  6.3.4 Simultaneous Conversations in a ReverberantRoom......Page 352
  6.4.1 Transmission of Reverberant Sound Througha Panel......Page 354
  6.4.3 Theory of Large Enclosures......Page 357
  6.4.4 Coupled Rooms......Page 359
  6.4.5 Reverberant Decay in Coupled Rooms......Page 360
 6.5 The Modal Theory of Room Acoustics......Page 361
  6.5.2 Modes for a Rectangular Room......Page 362
  6.5.3 Orthogonality of Modal Eigenfunctions......Page 364
  6.5.4 Modal Expansion of Functions......Page 365
  6.5.5 Field of a Point Source in a Room with Walls of Large Impedance......Page 366
  6.5.6 Acoustic Energy in a Room......Page 368
  6.5.7 Modal Description of Power Injection......Page 369
  6.6.1 The Modal Density......Page 370
  6.6.2 The Schroeder Cutoff Frequency......Page 372
  6.6.3 Approximation of Modal Sums by Integrals......Page 373
  6.6.4 Modal Averages of Squares of Eigenfunctions......Page 374
  6.6.5 Evaluation of Modal Integrals......Page 375
 6.7 Statistical Aspects of Room Acoustics......Page 376
  6.7.1 Frequency Correlation......Page 377
  6.7.2 The Poisson Distribution......Page 380
  6.7.3 Effect of Finite-Frequency Bandwidth......Page 382
 6.8 Spatial Correlations in Diffuse Sound Fields......Page 384
  6.8.1 The Spatial Autocorrelation Function for Acoustic Pressure......Page 385
  6.8.2 Spatial Averaging......Page 388
  6.8.3 Frequency Averaging Versus Spatial Averaging......Page 389
 6.9 Problems......Page 390
  7.1.1 Duct Cross-Sectional Eigenfunctions......Page 394
  7.1.3 Duct with Circular Cross Section......Page 396
  7.1.4 Cutoff Frequencies and Evanescent Modes......Page 397
  7.1.5 Point Source in a Duct......Page 398
 7.2 Lumped-Parameter Models......Page 400
  7.2.2 Acoustic Impedance......Page 401
  7.2.3 Acoustical Two-Ports......Page 402
  7.2.4 Continuous-Volume-Velocity Two-Port......Page 404
  7.3.1 Continuity of Pressure......Page 406
  7.3.2 Continuity of Volume Velocity......Page 408
  7.3.3 Reflection and Transmission at a Junction......Page 412
  7.4.1 The Helmholtz Resonator......Page 413
  7.4.2 Helmholtz Resonator as a Side Branch......Page 415
  7.4.3 Composite Example......Page 417
 7.5 Orifices......Page 418
  7.5.1 Matched-Asymptotic-Expansion Solution for Orifice Transmission......Page 419
  7.5.3 Helmholtz Resonator with Baffled Opening......Page 421
  7.5.4 Acoustic Inertance of a Circular Orificein a Thin Plate......Page 422
  7.5.5 Diffraction of Plane Wave by a Circular Orifice......Page 424
  7.6.1 Principle of Minimum Kinetic Energy......Page 425
  7.6.3 Effect of Relaxing of Constraints......Page 427
  7.6.4 Lower Bound for Acoustic Inertance......Page 428
  7.6.5 Flanged Opening in a Duct......Page 430
  7.6.7 End Corrections......Page 432
  7.6.8 Effective Neck Lengths of Helmholtz Resonators......Page 433
  7.6.9 Boundary Conditions at Open Ends of Ducts......Page 434
  7.7.1 The Transmission Matrix and Its Consequences......Page 436
  7.7.2 Insertion Loss......Page 437
  7.7.3 Reactive and Dissipative Mufflers......Page 438
  7.7.4 Helmholtz Resonators as Filters......Page 439
  7.7.5 Expansion-Chamber Muffler......Page 440
  7.7.6 Commercial Muffler Designs......Page 441
 7.8 Horns......Page 443
  7.8.1 The Webster Horn Equation......Page 446
  7.8.2 Salmon's Family of Horns......Page 447
  7.8.3 Concept of a Semi-Infinite Horn......Page 448
  7.8.4 The Cutoff Frequency......Page 449
  7.8.5 Other Considerations in Horn Design......Page 450
 7.9 Problems......Page 452
  8.1.1 Ray Paths in Moving Media......Page 460
  8.1.2 Fermat's Principle......Page 465
 8.2 Rectilinear Sound Propagation......Page 468
  8.2.1 Parametric Description of Wavefronts......Page 469
  8.2.2 Variation of Principal Radii of CurvatureAlong a Ray......Page 470
  8.2.3 Caustics......Page 471
  8.3.1 Refraction by Sound-Speed Gradients......Page 474
  8.3.2 Rays in a Medium with Constant-Sound-Speed Gradient......Page 476
  8.3.3 Refraction by Wind Gradients......Page 477
 8.4 Rays in Stratified Media......Page 479
  8.4.2 Channeling of Ray Paths......Page 480
  8.4.3 Rays in Fluids Without Ambient Flow......Page 482
  8.4.4 Abnormal Sound......Page 484
  8.5.1 Wave Amplitudes in Homogeneous Media......Page 488
  8.5.2 Energy Conservation Along Rays......Page 491
  8.6.1 Linear Acoustics Equations for Moving Media......Page 492
  8.6.2 Conservation of Wave Action......Page 494
  8.6.3 The Blokhintzev Invariant......Page 498
 8.7 Source Above an Interface......Page 501
  8.7.1 Sound Field Above the Interface......Page 502
  8.7.2 Field Below the Interface......Page 504
  8.8.1 General Geometrical Considerations......Page 506
  8.8.2 Ray-Tube Area After Reflection......Page 510
  8.8.4 Sound Beam Incident on a Sphere......Page 511
 8.9 Problems......Page 513
9 Scattering and Diffraction......Page 520
  9.1.1 Scattering by a Rigid Object......Page 521
  9.1.2 Scattering Cross Section......Page 524
  9.1.3 Higher-Frequency Scattering......Page 526
  9.1.4 Scattering by Inhomogeneities......Page 527
  9.1.5 Spherical Inhomogeneity......Page 530
  9.1.6 Inertia Effect for Freely Suspended Particle......Page 531
  9.1.7 Resonant Scattering......Page 532
 9.2 Monostatic and Bistatic Scattering: MeasurementConfigurations......Page 536
  9.2.1 Monostatic Pulse-Echo Sounding......Page 537
  9.2.2 Inhomogeneities and the Born Approximation......Page 539
  9.2.3 Scattering Volumes Delimited by Electroacoustic Transducers......Page 541
  9.2.4 Acoustic Radar Equation......Page 544
  9.2.5 Incoherent Scattering......Page 545
  9.2.6 The Echosonde Equation......Page 546
 9.3 The Doppler Effect......Page 550
  9.3.1 Doppler Shift for a Moving Source......Page 551
  9.3.2 Galilean Transformations......Page 553
  9.3.3 Echoes from Moving Targets......Page 554
  9.3.4 Doppler-Shift Velocimeters......Page 556
 9.4 Acoustic Fields Near Caustics......Page 560
  9.4.1 The Airy Function......Page 563
  9.4.2 Generalization to Inhomogeneous Media......Page 565
  9.4.3 Field Near a Turning Point......Page 567
  9.4.4 Phase Shift at a Caustic......Page 568
 9.5 Shadow Zones and Creeping Waves......Page 570
  9.5.1 Point Source Above a Locally Reacting Surface in a Stratified Medium......Page 571
  9.5.2 Residues Series for the Shadow Zone......Page 574
  9.5.3 Creeping Waves......Page 577
  9.5.4 Ray Shedding by a Creeping Wave......Page 579
 9.6 Source or Listener on the Edge of a Wedge......Page 580
  9.6.1 Source on Edge......Page 581
  9.6.2 Listener on the Edge......Page 582
 9.7 Contour-Integral Solution for Diffraction by a Wedge......Page 583
  9.7.1 Method of Images for Integer Wedge Index......Page 585
  9.7.2 Generalization to Noninteger Wedge Indices......Page 587
  9.8.1 The Geometrical Acoustics Portion of the Field......Page 589
  9.8.2 The Diffracted Wave......Page 592
  9.8.3 Asymptotic Expression for the Diffracted Wave......Page 593
  9.8.4 Physical Interpretation of the Diffracted Wave......Page 595
  9.9.1 Insertion Loss of Single-Edged Barriers......Page 599
  9.9.2 Far Field of a Source on the Side of a Building......Page 602
  9.9.3 Backscattering from an Edge......Page 604
 9.10 Problems......Page 606
  10.1.1 The Stress Tensor......Page 615
  10.1.2 The Energy Equation......Page 617
  10.1.3 Constitutive Relations for a Fluid......Page 618
  10.1.5 Transport Properties of Water......Page 621
  10.2.1 Linear Acoustic Equations......Page 622
  10.2.2 The Energy Conservation-Dissipation Corollary......Page 623
  10.2.3 Attenuation of Plane Sound Waves......Page 625
  10.3.1 Dispersion Relations for the Component Modes......Page 627
  10.3.3 Vorticity Mode......Page 630
  10.3.5 The Entropy Mode......Page 631
 10.4 Acoustic Boundary-Layer Theory......Page 632
  10.4.1 Boundary Conditions at a Solid Surface......Page 633
  10.4.2 Vorticity- and Entropy-Mode Fields Near a Solid Surface......Page 634
  10.4.3 Boundary Condition on the Acoustic-Mode Field......Page 636
  10.4.4 EnergyLossfromtheAcousticModeataBoundary......Page 637
  10.4.5 Plane-Wave Reflection at a Solid Surface......Page 638
  10.5.1 Propagation in Wide Ducts......Page 641
  10.5.2 Propagation in Narrow Tubes......Page 644
  10.5.3 Slab with Circular Pores......Page 647
 10.6 Viscosity Effects on Sound Radiation......Page 648
  10.6.1 Revision of the Kirchhoff-Helmholtz Theorem......Page 649
  10.6.2 Transversely Oscillating Rigid Bodies......Page 650
  10.6.3 Stokes Flow Limit......Page 651
  10.6.4 Thin-Boundary-Layer Approximation......Page 652
  10.6.5 Gutin's Principle......Page 654
  10.6.6 Helicopter Rotor Noise......Page 655
  10.7.1 Partitioning of Internal Energy......Page 659
  10.7.2 The Bulk Viscosity......Page 661
  10.7.3 Instantaneous Entropy Function......Page 662
  10.7.4 Fluid-Dynamic Equations with Relaxation lncluded......Page 663
  10.7.5 The Relaxation Equations......Page 665
  10.7.6 Numerical Values for the Constants of the Model......Page 666
  10.8.1 Linear Acoustic Equations for Air......Page 668
  10.8.2 Energy Corollary......Page 669
  10.8.3 Dispersion Relation for Plane Traveling Waves......Page 670
  10.8.4 Absorption by Relaxation Processes......Page 671
  10.8.5 Phase-Velocity Changes Due to RelaxationProcesses......Page 675
 10.9 Problems......Page 676
 11.1 Nonlinear Steepening......Page 681
  11.1.1 Plane Waves in Homogeneous Media......Page 682
  11.1.2 Steepening of Waveforms......Page 685
 11.2 Generation of Harmonics......Page 686
  11.2.1 Fourier-Series Representation......Page 687
  11.2.2 Conservation of Energy......Page 689
  11.3.1 The Rankine–Hugoniot Relations......Page 690
  11.3.2 Weak Shocks......Page 693
  11.3.3 The Equal-Area Rule......Page 694
  11.4.1 Plane-Wave Propagation of an N Wave......Page 696
  11.4.2 Dissipation of Acoustic Energy......Page 698
 11.5 Evolution of Sawtooth Waveforms......Page 699
 11.6 Nonlinear Dissipative Waves......Page 704
  11.6.1 Approximate Equations for Transient Plane Waves......Page 705
  11.6.3 The Burgers Equation......Page 706
  11.6.4 Rise Times and Thicknesses of Weak Shocks......Page 708
  11.6.5 Relaxation Effects on Shock Structure......Page 709
 11.7 Transition to Old Age......Page 712
  11.7.2 Solution of the Boundary-Value Problem......Page 713
  11.7.4 Transition from Sawtooth to Old Age......Page 715
  11.8.1 Corrected Travel Time Along Ray Path......Page 717
  11.8.2 Weak Shocks......Page 719
  11.8.3 Asymptotic Form of a Transient Pulse......Page 722
  11.9.1 N-Wave Propagation......Page 723
  11.9.2 Waves with Spherical Spreading......Page 724
 11.10 Ballistic Shocks: Sonic Booms......Page 726
  11.10.1 Linear Acoustic Model for Sound Generation by a Moving Body......Page 727
  11.10.2 Geometrical-Acoustics Interpretation......Page 730
  11.10.3 Nonlinear Modifications......Page 732
 11.11 Problems......Page 736
Appendix: Answers and Hints to Problems......Page 742
Name Index......Page 773
Subject Index......Page 782